A necessary and sufficient condition for the convexity of the generalized elliptic integral of the first kind with respect to Hölder mean
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Publication:5141742
DOI10.7153/jmi-2020-14-59zbMath1454.33016OpenAlexW3085341169MaRDI QIDQ5141742
Publication date: 18 December 2020
Published in: Journal of Mathematical Inequalities (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.7153/jmi-2020-14-59
Convexity of real functions in one variable, generalizations (26A51) Means (26E60) Elliptic functions and integrals (33E05)
Uses Software
Cites Work
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- A new form of the generalized complete elliptic integrals
- Ramanujan's cubic transformation inequalities for zero-balanced hypergeometric functions
- Optimal combinations bounds of root-square and arithmetic means for Toader mean
- Sharp bounds by the power mean for the generalized Heronian mean
- Parameter convexity and concavity of generalized trigonometric functions
- Concavity of the complete elliptic integrals of the second kind with respect to Hölder means
- Bounds for complete elliptic integrals of the second kind with applications
- A power mean inequality involving the complete elliptic integrals
- Inequalities for \(\alpha\)-fractional differentiable functions
- Optimal lower power mean bound for the convex combination of harmonic and logarithmic means
- Logarithmically complete monotonicity properties relating to the gamma function
- Generalized Hersch-Pfluger distortion function and complete elliptic integrals
- On Alzer and Qiu's conjecture for complete elliptic integral and inverse hyperbolic tangent function
- Convexity of the complete elliptic integrals of the first kind with respect to Hölder means
- Asymptotical formulas for Gaussian and generalized hypergeometric functions
- Monotonicity theorems and inequalities for the complete elliptic integrals
- Complete \(p\)-elliptic integrals and a computation formula of \(\pi_p\) for \(p=4\)
- Integral inequalities involving strongly convex functions
- Multiple-angle formulas of generalized trigonometric functions with two parameters
- Optimal bounds for Gaussian arithmetic-geometric mean with applications to complete elliptic integral
- Optimal bounds for the generalized Euler-Mascheroni constant
- Hermite-Hadamard type inequalities for fractional integrals via Green's function
- Quadratic transformation inequalities for Gaussian hypergeometric function
- Convexity with respect to Hölder mean involving zero-balanced hypergeometric functions
- Generalized elliptic integrals and modular equations
- Inequalities and infinite product formula for Ramanujan generalized modular equation function
- Generalization of Hermite-Hadamard type inequalities via conformable fractional integrals
- On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind
- Refinements of transformation inequalities for zero-balanced hypergeometric functions
- On generalized trigonometric functions with two parameters
- The number and stability of limit cycles for planar piecewise linear systems of node-saddle type
- Optimal Lehmer mean bounds for the Toader mean
- On the convergence of a modified regularized Newton method for convex optimization with singular solutions
- Asymptotical bounds for complete elliptic integrals of the second kind
- Bounds of the Neuman-Sándor mean using power and identric means
- High accuracy asymptotic bounds for the complete elliptic integral of the second kind
- Quantum Hermite-Hadamard inequality by means of a Green function
- Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term
- Discrete majorization type inequalities for convex functions on rectangles
- Majorization theorems for strongly convex functions
- Association of Jensen's inequality for \(s\)-convex function with Csiszár divergence
- Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
- Optimal two-parameter geometric and arithmetic mean bounds for the Sándor-Yang mean
- A note on generalized convex functions
- Hermite-Hadamard type inequalities for co-ordinated convex and qausi-convex functions and their applications
- On Cauchy-Schwarz inequality for \(N\)-tuple diamond-alpha integral
- Delay dynamic double integral inequalities on time scales with applications
- Monotonicity, convexity and inequalities involving the generalized elliptic integrals
- Convexity and concavity of the modified Bessel functions of the first kind with respect to Hölder means
- Sharp power mean inequalities for the generalized elliptic integral of the first kind
- Unstructured-mesh Galerkin finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equations on irregular convex domains
- Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type
- Sharp one-parameter geometric and quadratic means bounds for the Sándor-Yang means
- Approximation for the complete elliptic integral of the first kind
- Petrović-type inequalities for harmonic \(h\)-convex functions
- Integral majorization type inequalities for the functions in the sense of strong convexity
- The concept of coordinate strongly convex functions and related inequalities
- Sharp power mean bounds for two Sándor-Yang means
- Sharp power mean bounds for Sándor mean
- Precise estimates for the solution of Ramanujan's generalized modular equation
- Precise bounds for the weighted Hölder mean of the complete \(p\)-elliptic integrals
- Convexity properties of generalized trigonometric and hyperbolic functions
- On rational bounds for the gamma function
- On approximating the Toader mean by other bivariate means
- An optimal power mean inequality for the complete elliptic integrals
- On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities
- Monotonicity and functional inequalities for the complete \(p\)-elliptic integrals
- Sharp Landen transformation inequalities for hypergeometric functions, with applications
- Generalized convexity and inequalities
- Sharp function inequalities and boundness for Toeplitz type operator related to general fractional singular integral operator
- The optimal convex combination bounds of arithmetic and harmonic means in terms of power mean
- A power mean inequality for the Grötzsch ring function
- Hölder mean inequalities for the complete elliptic integrals
- Hölder mean inequalities for the generalized Grötzsch ring and Hersch-Pfluger distortion functions
- Monotonicity properties and bounds involving the complete elliptic integrals of the first kind
- A monotonicity property involving the generalized elliptic integral of the first kind
- Legendre-type relations for generalized complete elliptic integrals
- Landen inequalities for a class of hypergeometric functions with applications
- Notes on the complete elliptic integral of the first kind
- Inequalities for generalized trigonometric and hyperbolic functions with one parameter
- Converses of the Jensen inequality derived from the Green functions with applications in information theory
- Bounding the convex combination of arithmetic and integral means in terms of one-parameter harmonic and geometric means
- Monotonicity and inequalities involving zero-balanced hypergeometric function
- Stability and Hopf Bifurcation of a Delayed Prey–Predator Model with Disease in the Predator
- Boundedness of multilinear singular integral operator with non-smooth kernels and mean oscillation
- Monotonicity properties and bounds for the complete \(p\)-elliptic integrals